Class: MWF 12:00-12:50 in Altgeld Hall 159

Office hours: M 14:00-16:00 and W 19:00-20:00 in the Green Street Café

The textbook is Mathematical Thinking: Problem-Solving and Proofs by John P.D'Angelo and Douglas B. West.

Homework policy: You are not allowed any late homework. You will however be allowed to drop your lowest scoring homework for the computation of the final grade.

Distribution of scores, by assignment ex1 : 100 pts, 23 students, median 67, mean 68.7%, stdev 18.8% ex2 : 100 pts, 23 students, median 67, mean 68.5%, stdev 17.7% ex3 : 100 pts, 22 students, median 65, mean 66.1%, stdev 13.8%What? | Due date | Percentage | median | mean | standard derivation |

Homework | weekly, due Friday | 30% | |||

First midterm | Wednesday, September 28th | 15% | 67/100 | 68.7/100 | 18.8/100 |

Second midterm | Wednesday, October 26th | 15% | 67/100 | 68.5/100 | 17.7/100 |

Third midterm | Wednesday, November 30th (in class) | 15% | 65/100 | 66.1/100 | 13.8/100 |

Final | Monday, December 12th 7-10pm | 25% |

Lecture | Date | Summary | Assignments |

1 | 08/24 | Administrative issues. Group work on selected problems. | Prepare to present your group's progress to the class. |

2 | 08/26 | Presentation and discussion of group work problems. | Prepare to write a proof for your group's problem. Understand the solutions that were presented today. You will be asked to write a proof for one of these problems as well. |

3 | 08/29 | Presentation and discussion of group work problems | Understand the solutions that were presented today. |

4 | 08/31 | Presentation and discussion of group work problems | Understand the solutions that were presented today.Write a proof for your group's problem and the other problem assigned to you. (Due Wednesday 09/07!) |

5 | 09/02 | Inequalities | |

6 | 09/07 | Elementary set theory | Read the chapter about sets and finish the worksheet from class. (When you draw the Venn-diagram, draw the elements of the sets inside them! P(X) denotes the power set of X. Due Friday 09/09.) |

7 | 09/09 | Language and proofs - truth tables | Problem set 3. |

8 | 09/12 | Language and proofs - quantifiers and negating statements | |

9 | 09/14 | Language and proofs - negating statements | |

10 | 09/16 | Induction | Problem set 4 (due Wednesday 9/21!) |

11 | 09/19 | Induction (strong induction) | |

12 | 09/21 | Induction (method of descent) | Midterm 1 (due Wednesday 9/28) Solutions |

13 | 09/23 | Induction | |

14 | 09/26 | Induction | |

15 | 09/28 | Induction | |

16 | 09/30 | Induction, equivalence relations | Problem set 5 (due Friday 10/7) Selected Solutions |

17 | 10/03 | Injective and surjective maps | |

18 | 10/05 | Injective and surjective maps | |

19 | 10/07 | Injective and surjective maps, bijecitions and cardinality | Problem set 6 (due Friday 10/14). Question 1: all maps are well-defined! Selected Solutions |

20 | 10/10 | Bijecitions and cardinality: Cantor's diagonal argument. Combinatorial reasoning: permutations. | |

21 | 10/12 | Combinatorial reasoning: permutations and selections. | |

22 | 10/14 | Combinatorial reasoning: permutations and selections. | Problem set 7 (due Wednesday 10/19). |

23 | 10/17 | The Euclidean algorithm | |

24 | 10/19 | Euclidean algorithm, modular arithmetic | Midterm 2 (due Wednesday 10/26). Solutions |

25 | 10/21 | Euclidean algorithm, modular arithmetic | |

26 | 10/24 | Proof of the field axioms for Z/pZ | |

27 | 10/26 | RSA codes (compare Midterm 2 question 1), consequences of the field axioms | |

28 | 10/28 | Consequences of the field axioms ctd. | Problem set 8 (due Friday 11/4). |

29 | 10/31 | Pirates (group work) | |

30 | 11/02 | Groups, subgroups, left-cosets, the symmetric and the cyclic groups | |

31 | 11/04 | More about cosets. Proof that the order of a subgroup divides the order of the group. Definition of the order of a group element. Proof of Fermat's little theorem | |

32 | 11/07 | RSA-codes again. Euklid's prime number criterion (Z/pZ has no zero divisors). Proof that there are infinitely many prime numbers. | Here is a study guide for Midterm 3. |

33 | 11/09 | Graph theory, basic definitions | |

34 | 11/11 | Review | Problem set 9 (due Friday 11/18). |

35 | 11/14 | Review of set theory notation, Eulerian graphs | |

36 | 11/16 | Eulerian graphs | |

37 | 11/18 | A history of Euler's polyhedra formula | |

38 | 11/28 | canceled | Homework (due Friday Dec 2): Explain in your own words how RSA-codes (public-key codes) work. Who sends what to whom? What is secret, what is public? Why again does Problem (1d) of Midterm 2 prove that this works? Why is it possible to encode and decode something reasonably quickly? Why is it hard to break the code? Et cetera. This is not a proof writing question, I just want you to review the RSA-story. You are welcome to use any resources you have available. (This assignment will be worth 20 homework points.) |

39 | 11/30 | Third midterm | |

40 | 12/02 | ||

41 | 12/05 | Review | Final (due Monday 12/12). Tomorrow's office hours will be from 2:30 to 4:30. If you want to see me on Friday, you can sign up for that in class on Wednesday. |

39 | 11/30 | Third midterm |